The single handle is the 602 series. The two handle is 2852, 2702, or 2650 depending on the handle style and whether it has round or square escutcheons, but they all use the same body and operating parts.

We would like to replace the gold finish with something a little less 1989 , so I'm searching for replacement parts, but I wasn't sure what the heck this monstrosity was, so I really appreciate your response. I'm assuming the rough in valve for this set up is the 2700.